An elegiac poem tends to express feelings of great mourning. Therefore, an elegiac poem tends to be written about someone or something that has passed away and is gone forever. Tennyson's In Memoriam A. H. H. was written for his deceased friend Arthur Henry Hallam. Tennyson's poem proves elegiac given the focus of the poem's lines on death. After Hallam's death, Tennyson begins to consider life and death in ways that he may not have considered before.
The poem's diction (word choice) illustrates elegiac characteristics. The past is spoken of in past tense, and days and lives "cease to be." Tennyson's speaker even asks God to "remove his grief." This could be a way that Tennyson's speaker decides is the only way for him to move on from his grief. In this, Tennyson focuses upon language which illustrates death, loss, mourning, and grief.
On a side note, it is important to understand that Tennyson himself should necessarily not be identified as the speaker. Although he mourned the loss of Hallam, Tennyson's "I" should take on the voice of an "everyman" speaker. By doing so, Tennyson universalizes the sorrows and mournings associated with death. Humankind will all suffer the loss of those around them. Tennyson, therefore, seems to hope that this elegiac poem illustrates death and mourning as something which is natural. By doing this, one could argue that the use of the elegiac form helps others to find peace in the deaths they may face.
In regards to other elegiac aspects, the poem does not contain the typical extended metaphor, which some elegiac poems contain. Instead, the poem focuses simply on the death of a loved one and how the speaker attempts to come to terms with the death itself.